Grade 3 Practice Problems: Algebra
Examples from Standards Revision and GLEs
3A-26) Answer: 27
What 2-digit number is three times the sum of its digits? Write to help explain your best thinking using words, numbers, or pictures.
3A-25) Answer: $819.15
Dylan's mother offered to pay him to carry 14 bags of leaves to the compost pile. Dylan said he would do it if she would pay him 5 cents for the first bag, 10 cents for the second, and so on, doubling the amount with each bag. His mother only smiled and shook her head. How much would she have to pay? Write to help explain your best thinking using words, numbers, or pictures.
3A-24) Answer: 25 meteors
Some scientists believe they saw 52 meteors and others believe they saw 27. How many more did one group supposedly see than the other? Write to help explain your best thinking using words, numbers, or pictures.
3A-23) Answer: the 5th night
A crew of spiders moved into the scary old house and started working at once. They spun 2 webs on the first night, and 7 webs on the second night. On the third night they wove 12 webs. Every night they made 5 more webs than they had made the night before. If the spiders kept spinning in this way, on what night did they spin their 60th web? Write to help explain your best thinking using words, numbers, or pictures.
3A-22) Answer: Al-30 chips; John-14 chips
Al already has 16 more chips than John has. Al and John are playing a game with their friends. John and Al have won 44 chips altogether. How many chips has each boy won? Write to help explain your best thinking using words, numbers, or pictures.
3A-21) Answer: 5
Lyn and her friends made a pile of 31 snowballs this morning. Then the sun came out. It melted 1 snowball in the first hour, 2 snowballs in the second hour; and 4 snowballs in the third hour. Each hour the sun is melting twice as many snowballs as it did the hour before. If the sun keeps melting snowballs in this way, how many hours in all will it take the sun to melt the whole pile of snowballs? Write to help explain your best thinking using words, numbers, or pictures.
3A-20) Answer: 4 fleas, 3 ticks
Bowser, poor dog, has lost his collar; so he has a few uninvited fleas and ticks in his house. Each flea has 6 legs, and each tick has 8 legs. Not counting Bowser's legs, there are 48 legs in Bowser's house. There are the same number of flea legs as tick legs. How many fleas and how many ticks are there in Bowser's house? Write to help explain your best thinking using words, numbers, or pictures.
3A-19) Answer: 63
Papa's Pizza Place just opened for business. The good smells bring people into Papa's for pizza. Papa's sold 9 pizzas on the first day, 15 pizzas on the second day, and 21 pizzas on the third day. On the fourth day, Papa's sold 27 pizzas. Papa's business kept growing in the same way for a long time. How many pizzas did Papa's Pizza Place sell on the tenth day? Write to help explain your best thinking using words, numbers, or pictures.
3A-18) Answer: 40
Something terrible is happening in the third grade at Summers-coming School. A few students got the wigglegigs on Monday, and it seems to be spreading. On Tuesday, 2 more students caught the wigglegigs than on Monday. Each day after that, 2 more students caught the wigglegigs than the day before. On Friday, 12 students caught the wigglegigs. How many students caught the wigglegigs in five days? Write to help explain your best thinking using words, numbers, or pictures.
3A-17) Answer: the 6th week
MarIon was saving his money to buy a drum. He was earning money by pulling weeds in his neighbor's garden. He earned $0.50 the first week, and $1.00 the next week. The next week he earned $1.50, and he put it with the rest of his money. Each week he earned $0.50 more than he had earned the week before. If Marion kept earning money this way, in what week would he have a total of $10.50? Write to help explain your best thinking using words, numbers, or pictures.
3A-16) Answer: 24
Sarah and Kay are both collecting baseball cards. On Monday each of them got 3 cards. The next day Sarah got 5 and Kay got 4. On Wednesday Sarah got 7 and Kay got 6. On Thursday each girl got 9. If Sarah and Kay keep getting cards in the same way, how many cards will Kay get on the day that Sarah gets 15? Write to help explain your best thinking using words, numbers, or pictures.
3A-15) Answer: 22
When the leaves turned color, Hal and Dan began to sell pumpkins. On the first day, Hal and Dan each sold one pumpkin. The next day Hal sold 2 pumpkins and Dan sold 4. On the third day Hal sold 4 pumpkins and Dan sold 7. On the fourth day Hal sold 7 and Dan sold 10. It Hal and Dan kept selling pumpkins in the same way, how many pumpkins did Hal sell on the day Dan sold 19? Write to help explain your best thinking using words, numbers, or pictures.
3A-14) Answer: Daryl was 16, and Coralee was 8
When Daryl was 11 years old and his sister, Coralee, was 3, they watched a television show about hot-air balloons. Daryl started saving his money. When Daryl was twice as old as Coralee, he took her on a ride in a hot-air balloon. How old were Daryl and Coralee when they rode in the balloon? Write to help explain your best thinking using words, numbers, or pictures.
3A-13) Answer: 8 inches
Dean works with baby animals at a zoo. This week he measured a giraffe, an ape, and a tiger. The tiger had grown 4 inches less than the giraffe. The giraffe had grown twice as much as the ape. The baby ape had grown 6 inches since it was measured the last time. How many inches had the tiger grown? Write to help explain your best thinking using words, numbers, or pictures.
3A-12) Answer: 8 white, 6 red
Annie and Rob were playing a board game. During the game, they both collected white chips and red chips. Each white chip was worth points and each red chip was worth 3 points. At the end of the game, Annie had 14 chips worth 50 points in all. How many chips of each color did she have? Write to help explain your best thinking using words, numbers, or pictures.
3A-11) Answer: oak-6 feet high; maple-2 feet high
When Sue planted them, the oak tree was three times as high as the maple tree. Both trees grew about one foot a year. Now the oak tree is 13 feet high and the maple tree is 9 feet high. How high were the trees when Sue planted them? Write to help explain your best thinking using words, numbers, or pictures.
3A-10) Answer: 32 days old
Two koalas were born this month at the zoo. Kippy is 27 days old and Katy is 3 days old. Soon Kippy will be four times as old as Katy. How old will Kippy be then? Write to help explain your best thinking using words, numbers, or pictures.
3A-9) Answer: George-28; Ivan-17
Ivan stopped, but George kept running for 11 more laps. By the end of the run-a-thon, Ivan and George had run 45 laps around the school playground altogether. How many laps had each boy run? Write to help explain your best thinking using words, numbers, or pictures.
3A-8) Answer: Odds-red; evens-yellow
Make a row of 30 flowers. The first flower and every other one after that one are red. The rest of the flowers are yellow. What color is the 12th flower? What color is the 27th flower? What color are the odd numbers? What color are the even numbers? Write to help explain your best thinking using words, numbers, or pictures.
3A-7) Answer: 11 chicks; 14 eggs left
The brown hen laid 12 eggs. Seven of them have hatched. The red hen laid 13 eggs. Four of them have hatched. How many chicks in all? How many eggs are left? Write to help explain your best thinking using words, numbers, or pictures.
3A-6) Answer: most-Don; fewest-Donna
Joan has read six books. Karen has read one more book than Joan has read. Henry has read two fewer books than Joan has read. Don has read twice as many books as Henry has read. Donna has read five fewer books than Don has read. Who has read the most books? Who has read the fewest books? Write to help explain your best thinking using words, numbers, or pictures.
3A-5) Answer: down on the side of 15 mice & 2 cats; 1 mouse off first side; 5 mice off 1st side & 4 mice off 2nd side
Mice weigh one pound. Cats weigh ten pounds. Cats and mice are playing on the seesaw. On one side are fifteen mice and two cats. On the other side are three cats and four mice. Draw the seesaw as it would look that way. Explain two ways to make the seesaw balance. Write to help explain your best thinking using words, numbers, or pictures.
3A-4) Answer: 15 red total; 11 blue total; Carla has the most red blocks; Pat has the fewest blue
Carla has six red blocks and four blue blocks. Don has two fewer red blocks and one more blue block than Carla has. Pat has one more red block and three fewer blue blocks than Don has. How many red blocks in all? How many blue blocks in all? Who has the most red blocks? Who has the fewest blue blocks?
3A-3) Answer: The seesaw tipped down to the first side with 4 dogs. To balance 1 dog on the 1st side could exchange places with 3 mice & 3 cats of the 2nd side.
Mice weigh one pound. Cats weigh ten pounds. Dogs weigh one hundred pounds. The animals are playing on the see saw. On one side are four dogs, two cats, and one mouse. On the other side are two dogs, eight cats, and seven mice. Draw the seesaw with the animals on each side. What can the animals do to make the seesaw balance? Write to help explain your best thinking using words, numbers, or pictures.
3A-2) Answer: 4 students; 4 blue jars; 12 red jars; 42 paint jars
We have 24 students divided into 6 equal groups. They are sitting at tables painting. Each table has one yellow paint jar, twice as many red jars, and twice as many blue jars as red ones. How many students are in each group?____ How many blue jars are on each table?____ How many red jars in all?___ How many paint jars in all?___ Write to help explain your best thinking using words, numbers, or pictures.
3A-1) Answer: 8 pencils each - I put 40 into 5 equal groups of 8 pencils each.
We have 40 pencils to be divided equally among Bob, Darin, Carl, George, and Meg. How many pencils will each get? Write a sentence that tells what you had to do to get the answer. Write to help explain your best thinking using words, numbers, or pictures.
Expectations & Examples of Algebra from the 2008 Math Standards Revision (draft) - Grade 3
Represent multiplication as joining equal groups using words, numbers, pictures, physical materials, or equations, and translate among representations. Students may manipulate physical materials or draw pictures to find the total number of objects in equal sets or in an array. Picture representations may include finding the total distance resulting from equal jumps on a number line. Representations involving numbers and equations might include repeated addition, such as 3 x 4 = 4 + 4 + 4. Representations using words might include the use of the terms factors and products. Example:
Represent division as equal sharing or forming equal groups using words, numbers, pictures, physical materials, or equations, and translate among representations. The same physical materials and pictures used to demonstrate multiplication can be used to find a missing factor. Representations involving numbers and equations might include finding quotients with repeated subtraction or division sentences. Representations in words might include the terms quotient and remainder. Solve word problems that involve multiplication or division in a variety of contexts and explain solutions using words, numbers, pictures, physical materials, or equations.
Solve word problems that involve comparing fractions in a variety of contexts and explain solutions using physical materials, pictures, numbers, equations, or words. Examples:
Solve problems that involve attributes of two-dimensional figures and justify solutions using words, numbers, pictures, physical materials, or equations. Determine whether two expressions are equal and use “=” to denote equality. Examples:
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Examples of Algebraic Sense from the 2006 GLEs – Grade 3
Identify, describe, extend, or construct patterns of numbers based on a single addition or subtraction between terms. Identify, describe, extend, or construct patterns of figures or objects. Identify or write the missing elements in the beginning, middle, and/or end of a pattern. Identify a pattern that fits a given rule. Explain equality and the use of = in equations. Identify or write an equation for a given situation involving addition or subtraction. Identify or describe a situation that represents a given equation involving addition or subtraction. Determine when two expressions are equal and use = to denote equality. Describe a situation in which two expressions are equal. Read expressions and equations involving a single variable. Use mathematical symbols, including a single variable, to write expressions and equations to represent a given situation. Describe a situation that represents a given expression or equation that includes a single variable. Solve a one step equation with addition or subtraction using manipulatives, pictures, physical models, and/or symbols. Write and solve a one step equation using addition or subtraction in a given situation. Explain the meaning of the solution. |